Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

(i) \({{1} \over {4}} , -1\)

(ii) \(\sqrt{2}, {{1}\over{3}} \)

(iii) \(0, \sqrt{5}\)

(iv) \(1,1\)

(v) \({{-1} \over {4}},{{1} \over {4}} \)

(vi) \(4,1\)

Answer :

**(i)** \({{1} \over {4}} , -1\)

\(\Rightarrow \)Sum of the zeroes = \({{1} \over {4}}\) = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = -1 = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \)\(x^2 - {{1} \over {4}}x + (-1)\) => \(4x^2 - x - 4\)

**(ii)** \( \sqrt{2} , {{1}\over{3}}\)

\(\Rightarrow \)Sum of the zeroes = \( \sqrt{2}\) = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = \({{1} \over {3}}\) = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \)\(x^2 - \sqrt{2} x + {{1} \over {3}}\) \(\Rightarrow \) \(3x^2 - 3\sqrt{2}x + 1\)

**(iii)** \(0 , \sqrt{5}\)

\(\Rightarrow \)Sum of the zeroes = 0 = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = \(\sqrt{5}\) = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \)\(x^2 - 0x + ( \sqrt{5})\) => \(x^2 + \sqrt{5}\)

**(iv)** \(1 , 1\)

\(\Rightarrow \)Sum of the zeroes = 1 = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = 1 = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \) \(x^2 - 1x + 1\)

**(v)** \({{-1} \over {4}} , {{1} \over {4}}\)

\(\Rightarrow \) Sum of the zeroes = \({{-1} \over {4}}\) = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = \({{1} \over {4}}\) = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \) \(x^2 - {{-1} \over {4}}x + {{1} \over {4}}\) \(\Rightarrow \) \(4x^2 + x + 1\)

**(vi)** \(4 , 1\)

\(\Rightarrow \) Sum of the zeroes = 4 = \({{-b}\over {a}}\)

\(\Rightarrow \) Product of the zeroes = 1 = \({{c}\over {a}}\)

Polynomial can be formed by : \(x^2\) - (sum of zeroes)x + (product of zeroes)

\(\Rightarrow \) \(x^2 - 4x + 1\)

- NCERT solutions for class 10 maths chapter 1 Real Numbers
- NCERT solutions for class 10 maths chapter 1 Electricity, Light , Carbon and it's compounds
- NCERT solutions for class 10 maths chapter 2 Polynomials
- NCERT solutions for class 10 maths chapter 3 Pair of linear equations in two variables
- NCERT solutions for class 10 maths chapter 4 Quadratic Equations
- NCERT solutions for class 10 maths chapter 5 Arithmetic Progressions
- NCERT solutions for class 10 maths chapter 6 Triangles
- NCERT solutions for class 10 maths chapter 7 Coordinate Geometry
- NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry
- NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry
- NCERT solutions for class 10 maths chapter 10 Circles
- NCERT solutions for class 10 maths chapter 11 Constructions
- NCERT solutions for class 10 maths chapter 12 Areas related to circles
- NCERT solutions for class 10 maths chapter 13 Surface Areas and Volumes
- NCERT solutions for class 10 maths chapter 14 Statistics
- NCERT solutions for class 10 maths chapter 15 Probability

- NCERT solutions for class 10 science chapter 1 Chemical Reactions and Equations
- NCERT solutions for class 10 science chapter 2 Acids, Bases and Salts
- NCERT solutions for class 10 science chapter 3 Metals and Non Metals
- NCERT solutions for class 10 science chapter 4 Carbon and its Compounds
- NCERT solutions for class 10 science chapter 5 Periodic Classification of Elements
- NCERT solutions for class 10 science chapter 6 Life Processes
- NCERT solutions for class 10 science chapter 7 Control and Coordination
- NCERT solutions for class 10 science chapter 8 How do Organisms Reproduce
- NCERT solutions for class 10 science chapter 9 Heredity and Evolution
- NCERT solutions for class 10 science chapter 10 Light Reflection and Refraction
- NCERT solutions for class 10 science chapter 11 Human Eye and Colorful World
- NCERT solutions for class 10 science chapter 12 Electricity
- NCERT solutions for class 10 science chapter 13 Magnetic Effect of Electric Current
- NCERT solutions for class 10 science chapter 14 Sources of Energy
- NCERT solutions for class 10 science chapter 15 Our Environment
- NCERT solutions for class 10 science chapter 16 Management of Natural Resources